Download Introduction ( 5 min )

Introduction ( 5 min )
Post Geometry Quote/Joke of the Day: “Without geometry life is pointless”
Have the students discuss different triangles the see in their daily lives. Have them give an
example from the city, in their house and in nature. Ask them to answer the question: What aspects of
these triangles would you use to classify and compare them?
Daily Review ( 10 min )
Go over the homework due today.
Have students do Algebra review questions 13, 17, 19-21 on p. 258 that are in correlation to the
types of algebra they will use to find parts of triangles.
Daily Objective
Introduce Triangles and Angles classifications with Vocabulary: State Standard 4.12.1, 1.12.8,
2.12.2, 2.12.3, 2.45.6, 4.8.7
Concept and Skill Development and Application ( 15 min )
The students will classify triangles by sides and/or angles. Go over the classifications of triangles
and have students write down each type and its definition in math journals. Have students recite the
parts of a triangle and what interior/exterior angles are.
Key Vocabulary:
Equilateral Triangle: 3 congruent sides
Isosceles Triangle: At least 2 congruent sides
Scalene Triangle: No congruent sides
Acute Triangle: 3 acute (<90 degrees) angles
Equiangular Triangle: 3 congruent angles
Right Triangle: 1 right (90 degrees) angle
Obtuse Triangle: 1 obtuse (>90 degrees) angle
Vertex: Each of the three points joining the sides of a triangle
Adjacent sides: Two sides sharing a common vertex
Leg: In a right triangle it is one of the two sides that form the 90 degree angle. In an isosceles
with only two congruent sides, then these sides are also legs.
Hypotenuse: The side opposite of the right angle
Base: The third side of an isosceles triangle with two congruent sides.
Go over the Triangular Sum Theorem and Exterior Angle Theorem. Guide students to solve 2-3
examples which include having students use given angle measurements to find interior/external
unknown angles.
Triangle Angle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180.
(1) Find the measure of ∠C.
As with all problems, we must first use the facts that are given to us. Using the diagram, we are
given that
Since our goal is to find the measure of ∠C, we can use the Triangle Angle Sum Theorem to
solve for the missing angle. So we have
Using the angle measures we were given, we can substitute those values into our equation to get.
Having ∠C measure out to 26° satisfies the property that the sum of the interior angles of a
triangle is 180°.
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two
remote interior angles.
Adding the measures of the two remote interior angles of a triangle gives the measure of the
exterior angle.
Example
(1) Find the measures of ∠1 and ∠2 in the figure below.
(2)
First, we can solve for m∠1 since we are given the measure of two angles of that triangle. This
part of the problem is similar to the examples we have already done above. Let's begin with the
statements of what we are given, which are:
Now, we can solve for m∠1 by using the Triangle Angle Sum Theorem. So we have
In order to solve for the measure of ∠2, we will need to apply the Exterior Angle Theorem. We
know that the two remote interior angles in the figure are ∠S and ∠A. Thus, by the Exterior
Angle Theorem, the sum of those angles is equal to the measure of the exterior angle. We have
While not always necessary, we can check our solution using our previous knowledge of lines.
We see that ∠1 and ∠2 make up ray AK. And since straight lines have 180° measures, we know
that the sum of ∠1 and ∠2 must be 180. Let's check to make sure:
(2) Find m∠B.
Let's take a look at the information we have been given first.
Right off the bat, we can apply the Exterior Angle Theorem to help us solve the problem.
The question asked for m∠B. The variable x alone does not tell us what the measure of the angle
is. So, we must plug x = 4 into our equation for m∠B:
Guided/Independent/Group Practice ( 15 min )
Have students group into pairs and each draw and classify a triangle we learned about in class in
their Math Journals. On the next page in their journals I will ask them to construct a Frayer Model about
the triangle they drew with the following categories; Definition, Characteristics, Real Life Examples, and
Other Shapes that are Made Up of Triangles. Then present it to their partner. Instruct them to together
come up with some out-of-the-box observations about their triangles to contribute to the class
discussion.
As a class, complete a Concept Definition Map for Acute, Equiangular, Right and Obtuse
triangles. Ask the students to share any out-of-the-box observations they had from the small group
project.
Homework
Pg. 198 Problems: 10-15, 17-21 odd, 22-26, 36, 38, 41-44, 47
Closure ( 5 min )
Have students write in their math journals about what they liked and disliked about the lesson
today and one item/formula that they thought was most important. Also have the student do the
following: Use one of the vocabulary words from today and explain a real example from your life.
Remind the students about the Parking Lot and go over any questions from the previous days
Parking Lot. Also go over any announcement you have for the class.